#### Abstract

Let *G* be a finite group. We classify *G*-equivariant flow equivalence of non-trivial irreducible shifts of finite type in terms of

(i) elementary equivalence of matrices over **Z***G* and

(ii) the conjugacy class in **Z***G* of the group of *G*-weights of cycles based at a fixed vertex.

In the case *G* = **Z**/2, we have the classification for *twistwise flow equivalence*. We include some algebraic results and examples related to the determination of E(**Z***G*) equivalence, which involves K_{1}(**Z***G*).

#### Recommended Citation

Boyle, Mike and Sullivan, Michael C. "Equivariant Flow Equivalence of Shifts of Finite Type by Matrix Equivalence over Group Rings." (Jan 2005).

## Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in

Proceedings of the London Mathematical Societyfollowing peer review. The definitive publisher-authenticated version "Equivariant Flow Equivalence for Shifts of Finite Type, by Matrix Equivalence Over Group Rings,"Proceedings of the London Mathematical Society, 91(1):184-214, is available online at: http://dx.doi.org/10.1112/S0024611505015285.